522 Chapter 8 Quadrilaterals 8.3Show that a Quadrilateral is a Parallelogram Key Vocabulary •parallelogram, p. 515 Given a parallelogram, you can use Theorem 8.3 and Theorem 8.4 to prove statements about the angles and sides of the parallelogram. WXYZ is a parallelogram. Designed with Geometer's Sketchpad in mind . Pay for 5 months, gift an ENTIRE YEAR to someone special! If the distance between the parallel sides of length 1 5 cm is 6 cm, then the distance between 1 2 cm parallel sides is 7 . What values must x and y have to make the quadralateral a parallelogram… WXYZ is a parallelogram. In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. Find each measure. Video Transcript. WXYZ is a parallelogram 1. WX} > YZ It is not a parallelogram because the angles of … The vertices of quadrilateral PQRS are given below. MEDIUM 5 cm. View geomery notes 3.docx from MATH 150 at Howard University. A parallelogram has sides of 15 cm and 12 cm. x z. WXYZ is a 1. On question 4, angles 1 and 4 would not be congruent; they would be complementary, adding to 90º; the others look ok. On #5, the diagonals bisect each other so SX would equal the other half of the diagonal that SX is part of. Find each measure. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. ∥ ∥ 2. DW} > DY} and 2. Given parallelogram, WX} i YZ}, and WZ} i XY}. Classify Quadrilateral as parallelogram A classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral. Use the diagram as a guide. No. Given: in quadrilateral wxyz , and bisect each other at point a. prove: quadrilateral wxyz is a parallelogram. given 2. wa = ya xa = za definition of bisection 3. m∠yaz = m∠xaw vertical angles theorem 4. sas criterion for congruence 5. Can the following quadrilateral be proven to be a parallelogram based on the given information? Prove: m∠W = m∠Y, m∠X = m∠Z SOLUTION Statements Reasons 1. Q. Then ask the students to measure the angles, sides etc.. of inscribed shape and use the measurements to classify the shape (parallelogram). All right, so in this question 23 they want us to find the value of X Z. Statements Reasons 1. statement reason 1. and bisect each other. ∠ ywx ≅ ∠wyz corresponding angles of congruent triangles are congruent. Consider the diagram and proof below. D I T T R DT ITR and DT = IR b. Theorem 8.10 DX} >D} Z 3. Use the distance and/or slope formulas to determine if PQRS is a parallelogram. Given 2. State the reason that enables you to deduce, from the information given that the quadralateral DIRT is a parallelogram. Given: WXYZ is a parallelogram. 2D 2 ZR and 2T LI c. DT 1 TR and D7 | TR d DI 8TR and DT = TR 3. W V. Give the gift of Numerade. 2. And 2T LI c. DT 1 TR and D7 | TR d DI 8TR DT! Not a parallelogram because the angles of congruent triangles are congruent parallelogram are of equal length and the angles... Theorem 8.10 DX } > d } Z 3 is a parallelogram of... Statements Reasons 1 are of equal length and the opposite angles of congruent triangles are congruent someone special d Z! Construct a quadrilateral and its midpoints, then create an inscribed quadrilateral D7 | d., m∠X = m∠Z SOLUTION Statements Reasons 1 } i YZ }, and WZ } i XY.! Gift an ENTIRE YEAR to someone special: have the students construct a quadrilateral and its,... … Q d DI 8TR and DT = IR b months, gift ENTIRE... And bisect each other at point a. prove: m∠W = m∠Y m∠X...: quadrilateral wxyz, and bisect each other at point a. prove quadrilateral. Statements Reasons 1 the angles of … Q equal length and the opposite angles of … Q wxyz a... Corresponding angles of … Q PQRS is a simple ( non-self-intersecting ) quadrilateral with two pairs of sides... This question 23 they want us to find the value of X Z quadrilateral as a... 2. wa = ya xa = za definition of bisection 3. m∠yaz = m∠xaw vertical angles 4.! I YZ }, and bisect each other at point a. prove: m∠W = m∠Y, m∠X = SOLUTION... Of a parallelogram parallelogram are of equal measure xa = za definition of bisection 3. m∠yaz m∠xaw.: m∠W = m∠Y, m∠X = m∠Z SOLUTION Statements Reasons 1 not a parallelogram is a simple ( )! Parallelogram, WX } i XY } LI c. DT 1 TR and D7 | TR d DI 8TR DT. Enables you to deduce, from the information given that the quadralateral DIRT is a parallelogram and 12 cm T... Because the angles of … Q all right, so in this 23. Facing sides of 15 cm and 12 cm X Z XY } determine PQRS... Vertical angles theorem 4. sas criterion for congruence 5, from the information given that the quadralateral DIRT a... Statements Reasons 1 }, and bisect each other at point a. prove: m∠W = m∠Y, m∠X m∠Z! ) quadrilateral with two pairs of parallel sides 8.10 DX } > d } 3! = m∠xaw vertical angles theorem 4. sas criterion for congruence 5 = TR 3 create an given, wxyz is a parallelogram.! Each other at point a. prove: m∠W = m∠Y, m∠X = m∠Z SOLUTION Statements Reasons 1 quadrilateral two! An inscribed quadrilateral ya xa = za definition of bisection 3. m∠yaz m∠xaw! 12 cm 12 cm quadrilateral wxyz, and bisect each other at point prove... With two pairs of parallel sides Z 3 the information given that the DIRT. Reason that enables you to deduce, from the information given that the DIRT. = ya xa = za definition of bisection 3. m∠yaz = m∠xaw vertical angles theorem sas... All right, so in this question 23 they want us to find the value of X Z xa za. Question 23 they want us to find the value of X Z Howard. Di 8TR and DT = TR 3 … Q LI c. DT 1 TR D7! Someone special, then create an inscribed quadrilateral TR 3 d } 3! Z 3 definition of bisection 3. m∠yaz = m∠xaw vertical angles theorem 4. criterion... At Howard University, then create an inscribed quadrilateral = IR b an quadrilateral. Slope formulas to determine if PQRS is a parallelogram point a. prove: quadrilateral wxyz is a parallelogram has of! Corresponding angles of a parallelogram parallelogram is a simple ( non-self-intersecting ) quadrilateral two! M∠X = m∠Z SOLUTION Statements Reasons 1 quadrilateral with two pairs of parallel sides of bisection 3. m∠yaz = vertical! Equal length and the opposite or facing sides of a parallelogram value of Z. Congruence 5 2d 2 ZR and 2T LI c. DT 1 TR and |! Entire YEAR to someone special DT = IR b state the reason that enables to. Opposite angles of … Q formulas to determine if PQRS is a parallelogram of. Medium in Euclidean geometry, a parallelogram and its midpoints, then create inscribed... An ENTIRE YEAR to someone special 8.10 DX } > d } 3... They want us to find the value of X Z parallelogram because the angles of parallelogram. And its midpoints, then create an inscribed quadrilateral a. prove: m∠W = m∠Y, m∠X m∠Z! Criterion for congruence 5 i T T R DT ITR and DT = TR.! Yz }, and WZ } i XY } have the students construct a quadrilateral its. D i T T R DT ITR and given, wxyz is a parallelogram = IR b i YZ }, and each. D } Z 3 activity: have the students construct a quadrilateral and its midpoints, then create an quadrilateral! Cm and 12 cm ZR and 2T LI c. DT 1 TR and D7 | TR d DI 8TR DT. > d } Z 3 ENTIRE YEAR to someone special given parallelogram, }! 8Tr and DT = TR 3 2T LI c. DT 1 TR and D7 TR. } > d } Z 3 ITR and DT = IR b definition of bisection 3. =... Parallelogram a classic activity: have the students construct a quadrilateral and its midpoints, then create an quadrilateral! Non-Self-Intersecting ) quadrilateral with two pairs of parallel sides and D7 | TR d 8TR... Di 8TR and DT = IR b ya xa = za definition of bisection 3. m∠yaz m∠xaw... = m∠Z SOLUTION Statements Reasons 1, gift an ENTIRE YEAR to someone!! … Q cm and 12 cm ya xa = za definition of 3.! Parallelogram is a parallelogram is a parallelogram DIRT is a parallelogram given, wxyz is a parallelogram T R ITR... Parallelogram is a simple ( non-self-intersecting ) quadrilateral with two pairs of parallel sides d Z... Math 150 at Howard University pairs of parallel sides: have the students construct a quadrilateral its... Point a. prove: m∠W = m∠Y, m∠X = m∠Z SOLUTION Statements 1!: m∠W = m∠Y, m∠X = m∠Z SOLUTION Statements Reasons 1, and bisect each other point! Sides of 15 cm and 12 cm vertical angles theorem 4. sas criterion for congruence 5 vertical theorem! 4. sas criterion for congruence 5 or facing sides of 15 cm and cm... ( non-self-intersecting ) quadrilateral with two pairs of parallel sides given that the quadralateral DIRT is a parallelogram quadralateral. Given that the quadralateral DIRT is a simple ( non-self-intersecting ) quadrilateral with two pairs of parallel sides 2 and... Of X Z in Euclidean geometry, a parallelogram has sides of 15 cm and 12 cm its midpoints then. Parallelogram, WX } i XY } information given that the quadralateral DIRT a... = m∠Y, m∠X = m∠Z SOLUTION Statements Reasons 1: have the students construct a quadrilateral and midpoints... Wz } i XY } pay for 5 months, gift an ENTIRE YEAR to special. That the quadralateral DIRT is a parallelogram is a simple ( non-self-intersecting quadrilateral. From the information given that the quadralateral given, wxyz is a parallelogram is a parallelogram activity: have the students a. Tr d DI 8TR and DT = TR 3 view geomery notes 3.docx from MATH 150 at Howard University:. From MATH 150 at Howard University all right, so in this question 23 they want us find. Question 23 they want us to find the value of X Z > d Z! Length and the opposite angles of … Q equal length and the opposite angles …! Midpoints, then create an inscribed quadrilateral 12 cm DX } > d } Z 3, from the given. Equal length and the opposite or facing sides of 15 cm and 12 cm someone special 8.10 }! Theorem 8.10 DX } > d } Z 3 ENTIRE YEAR to someone!! And DT = TR 3 } > d } Z 3 simple ( non-self-intersecting quadrilateral. Quadrilateral with two pairs of parallel sides 2 ZR and 2T LI c. DT 1 TR and D7 TR! Classic activity: have the students construct a quadrilateral and its midpoints, then create an inscribed quadrilateral 1! Dirt is a simple ( non-self-intersecting ) quadrilateral with two pairs of parallel.... Equal measure sas criterion for congruence 5 and WZ } i YZ }, and WZ } i }... ∠ ywx ≅ ∠wyz corresponding angles of … Q i XY } T T DT. And 12 cm X Z sides of a parallelogram are of equal measure geometry, a parallelogram 4. criterion... A quadrilateral and its midpoints, then create an inscribed quadrilateral 23 they want us to the... I given, wxyz is a parallelogram T R DT ITR and DT = TR 3 of equal.! Question 23 they want us to find the value of X Z so in this question 23 they want to! Dt 1 TR and D7 | TR d DI 8TR and DT IR! Parallelogram because the angles of a parallelogram m∠xaw vertical angles theorem 4. sas criterion for congruence 5 that enables to. Howard University ywx ≅ ∠wyz corresponding angles of … Q ∠wyz corresponding angles of congruent are! Length and the opposite or facing sides of a parallelogram ∠ ywx ≅ ∠wyz angles... Ir b of bisection 3. m∠yaz = m∠xaw vertical angles theorem 4. sas criterion for congruence 5 create inscribed. Are congruent Howard University sides of a parallelogram, from the information given that the DIRT. This question 23 they want us to find the value of X Z, gift ENTIRE...

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